We consider the following 2-step procedure given as an interpretation of \(g\)  in [1]}: we first sample \(p \sim \mathcal {D}_{\phi }\) , then construct a random \(B \subseteq A\)  by taking each element of \(A\)  independently with probability \(p\) . The probability that any given \(B \subseteq A\)  is selected by the procedure is then precisely
\(\int _{0}^1\frac{\phi e^{\phi p}}{e^\phi - 1}p^{|B|}(1-p)^{|A|}\,dp = m_{|A|,|B|}\,.\) 
